Chapter 5 STAT 208: Linear Statistical Models

This chapter contains past exam problems of STAT 208: Linear Statistical Models. There are four textbooks used for this class, Christensen (2011), Graybill (2000), Searle (1997) and Kutner et al. (2005). Belowing listed the STAT 208 part of syllabus for First Year Exam (2020).

  • Basic notions of linear algebra, e.g., vector spaces, column and null spaces of a matrix, inverse and generalized inverse, solutions to systems of linear equations, basis, orthogonal matrices, idempotent matrices, eigenvalues and eigenvectors.

  • Definition and examples of the general linear model, including simple and multiple linear regression, analysis of variance, and analysis of covariance models.

  • Ordinary and generalized Least Squares Estimation. Estimable functions. Best linear unbiased estimators and the Gauss-Markov Theorem.

  • Distribution Theory. Class notes but available in many books. Covariances. Properties of covariances. Quadratic forms. Expectations of quadratic forms. Multivariate Normal distribution and its properties. Orthogonal transformations of MVN vectors. Partitions and conditional distributions. Quadratic forms in Multivariate Normal Variables and its distributions. Cochran’s theorem. Non-central F distribution.

  • Maximum likelihood estimation, interval estimation and hypothesis testing under the Gaussian Gauss-Markov model.

  • You should also be familiar with fitting linear models using R. Class notes for examples.

References

Christensen, Ronald. 2011. Plane Answers to Complex Questions: Theory of Linear Models. 4th ed. New York City, NY: Springer Texts in Statistics.

Graybill, Franklin. 2000. Theory and Application of the Linear Model. Pacific Grove, CA: Duxbury.

Kutner, Michael, Christopher Nachtsheim, John Neter, and William Li. 2005. Applied Linear Statistical Models. 5th ed. New York, NY: McGraw-Hill Irwin.

Searle, Shayle. 1997. Linear Models. New York, NY: Wiley.